Fluid simulation · muse-ember
Output generated Cost / run $0.0297 Runtime 85.4s
Prompt for this run
Build an interactive 2D fluid-and-dye simulation on a full-screen canvas. Use HTML, CSS, and JavaScript as needed. Write it to `index.html` in the current working directory using your file tools. Inline your own CSS and JavaScript. Do not use external assets, CDNs, or network requests. No third-party libraries are provided. Required behavior: - Maintain a velocity field and a colored dye field. Advect dye through the moving fluid so it forms persistent swirling flow; a collection of independent fading particles is not sufficient. - Dragging injects dye and momentum in the drag direction. Momentum and dye remain visible after the pointer is released and gradually dissipate. Approximate fluid behavior is acceptable; choose the numerical method and Canvas 2D or WebGL implementation. - Seed the initial scene with a small amount of colored dye and motion so the simulation is visible on load. - Provide a color selector, Pause/Resume, and Clear. Clear removes dye and resets velocity; the next drag can start a new flow. - Bound simulation resolution and work per frame so controls remain responsive at a 1200 by 800 viewport. Verify: Drag through the canvas and sample the flow after release. Check that dye follows the drag, continues swirling, and responds to a second drag in another direction. Use Clear, then drag again to check that a fresh flow can start.
TAKE IT TO CODE
A single self-contained HTML file — copy it and open in any browser, or reuse the prompt with your own pi-agent run.
METRICS
Transcript · 45 messages
Build an interactive 2D fluid-and-dye simulation on a full-screen canvas. Use HTML, CSS, and JavaScript as needed. Write it to `index.html` in the current working directory using your file tools. Inline your own CSS and JavaScript. Do not use external assets, CDNs, or network requests. No third-party libraries are provided. Required behavior: - Maintain a velocity field and a colored dye field. Advect dye through the moving fluid so it forms persistent swirling flow; a collection of independent fading particles is not sufficient. - Dragging injects dye and momentum in the drag direction. Momentum and dye remain visible after the pointer is released and gradually dissipate. Approximate fluid behavior is acceptable; choose the numerical method and Canvas 2D or WebGL implementation. - Seed the initial scene with a small amount of colored dye and motion so the simulation is visible on load. - Provide a color selector, Pause/Resume, and Clear. Clear removes dye and resets velocity; the next drag can start a new flow. - Bound simulation resolution and work per frame so controls remain responsive at a 1200 by 800 viewport. Verify: Drag through the canvas and sample the flow after release. Check that dye follows the drag, continues swirling, and responds to a second drag in another direction. Use Clear, then drag again to check that a fresh flow can start.
thinking
Designing a self-contained Canvas 2D fluid simulation using stable Navier-Stokes with semi-Lagrangian advection and Jacobi pressure solve on a low-resolution grid.
index.html (11966 bytes)Successfully wrote to index.html
thinking
{"action":"inspect"}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.","images":"attached"}
thinking
{"action":"drag","x":300,"y":500,"toX":900,"toY":300}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n50 fps · 132×88 grid","images":"attached"}
thinking
{"action":"screenshot"}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n46 fps · 132×88 grid","images":"attached"}
thinking
{"action":"motion"}Frame 1, +0ms
[Browser image supplied to model]
Frame 2, +668ms
[Browser image supplied to model]
Frame 3, +1296ms
[Browser image supplied to model]
Frame 4, +1925ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n51 fps · 132×88 grid","images":"attached"}
thinking
Analyzing fluid simulation velocity decay and Jacobi projection to diagnose why motion stops immediately after release.Checking Jacobi projection and velocity decay to explain the lack of sustained motion.Diagnosing dye saturation masking motion and adjusting injection strength and rendering mapping.
{"path":"index.html","edits":[{"oldText":"var u,v, p, dyeR,dyeG,dyeB, tmpU,tmpV, tmpR,tmpG,tmpB, curlF;","newText":"var u,v, p, divF, dyeR,dSuccessfully replaced 6 block(s) in index.html.
thinking
{"path":"index.html","edits":[{"oldText":" var vx=(dx/cellW)*(1000/dtMs)*0.055; // cells/sec scaled -> impulse\n var vy=(dy/cellH)*(1000/dSuccessfully replaced 1 block(s) in index.html.
{"action":"reload"}Frame 1, +1ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.","images":"attached"}
thinking
{"action":"drag","x":250,"y":550,"toX":950,"toY":250}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n37 fps · 132×88 grid","images":"attached"}
thinking
{"action":"motion"}Frame 1, +1ms
[Browser image supplied to model]
Frame 2, +771ms
[Browser image supplied to model]
Frame 3, +1500ms
[Browser image supplied to model]
Frame 4, +2208ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n36 fps · 132×88 grid","images":"attached"}
thinking
Analyzing weak motion by checking drag event timing, dtMs impact, and velocity cancellation from projection after a localized splat.Deriving the discrete Laplacian sign and factor to correct the projection iteration.
{"path":"index.html","edits":[{"oldText":" fpsAcc+=dt; fpsN++; fpsT+=dt;\n if(fpsT>0.5){ stat.textContent=(fpsN/Math.max(0.001,fpsAcc)).toSuccessfully replaced 1 block(s) in index.html.
{"action":"reload"}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.","images":"attached"}
thinking
{"action":"screenshot"}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n51 fps · 132×88 grid · vmax 17.8 dmax 0.85","images":"attached"}
thinking
{"action":"drag","x":200,"y":600,"toX":1000,"toY":200}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n41 fps · 132×88 grid · vmax 27.2 dmax 1.21","images":"attached"}
thinking
{"action":"screenshot"}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n45 fps · 132×88 grid · vmax 9.6 dmax 0.71","images":"attached"}
thinking
{"action":"drag","x":900,"y":600,"toX":300,"toY":200}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n37 fps · 132×88 grid · vmax 15.1 dmax 0.93","images":"attached"}
thinking
{"action":"click","x":672,"y":40}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n50 fps · 132×88 grid · vmax 6.9 dmax 0.77","images":"attached"}
thinking
{"action":"drag","x":300,"y":300,"toX":900,"toY":500}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n43 fps · 132×88 grid · vmax 18.7 dmax 1.03","images":"attached"}
thinking
{"action":"click","x":610,"y":40}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nResume\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n50 fps · 132×88 grid · vmax 9.1 dmax 0.63","images":"attached"}
thinking
{"action":"click","x":610,"y":40}Frame 1, +0ms
[Browser image supplied to model]
{"console":[],"dom":"FLUID · DYE\nDye\nPause\nClear\nSeed swirl\nDrag to inject dye & momentum — release and watch it swirl, then drag another way.\n45 fps · 132×88 grid · vmax 9.1 dmax 0.63","images":"attached"}
thinking
{"command":"ls -lh index.html; grep -iE \"http://|https://|cdn|src=|link rel\" index.html || echo \"no external refs\""}-rw-r--r-- 1 node node 13K Nov 10 01:06 index.html no external refs
thinking
Built `index.html` — a single self-contained fluid-and-dye simulation (no external assets/CDNs). **Implementation:** Canvas 2D with a bounded 132×~88 semi-Lagrangian Navier–Stokes solver: velocity (u,v) + RGB dye fields, advection of dye through the velocity field, Jos Stam projection (Jacobi pressure solve, 24 iterations), vorticity confinement, solid-wall boundaries, gradual velocity/dye dissipation. Dye is rendered from a low-res offscreen `ImageData` scaled up with smoothing. Dragging splats dye (from the color picker) and momentum in the drag direction; the scene is seeded on load with opposing vortices/a swirl ring. HUD provides color selector, Pause/Resume, Clear (zeroes dye+velocity), and Seed swirl, plus an fps/grid/vmax readout. Work per frame is bounded (fixed grid, clamped dt) for responsiveness at 1200×800. **Verified in the browser (1200×800):** - Initial load: seeded dye/swirl visible immediately, ~50 fps, no console errors. - Drag diagonal: pink dye streak followed the drag direction. - After release: sampled flow after ~1s — streak curled/swirled (vmax decaying gradually from ~27 to ~10), confirming persistent advection, not just fading particles. - Second drag in the opposite direction: formed an X and deformed the existing flow. - Clear: canvas emptied; subsequent drag started a fresh flow (vmax ~18.7). - Pause toggled to Resume and back. **Unverified:** color-picker change to a non-default color (selector present but not changed in tests), touch input, and long-term (>few seconds) dissipation timing.